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Visualizing Complex Differential with Mapping Diagram

Visualizing Complex Differential with Mapping Diagram
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2015-12-10 06:01
FunctionCalculusComplex Number
This example uses a mapping diagram to visualize complex differential. It involves the derivative of complex functions and dynamically adjusts parameters to observe changes in the function's graph. Main commands used include Sequence, CurveCartesian, Vector, Textfield, Intersect, and Derivative. Suitable for complex analysis studies in university mathematics.

GeoGebra Commands & Parameters

  1. Sequence((r * (cos(t) + (sin(t) * ί))), t, -3.141592653589793, 3.141592653589793, 0.5235987755982988) → z_*
  2. Sequence((x(Element[fz_*, k]), y(Element[fz_*, k]), height_{image}), k, 1, 12) → fpoint_*
  3. Sequence(Vector[Element[z_*, j], Element[fpoint_*, j]], j, 1, 12) → fvec_*
  4. CurveCartesian((r * cos(t)), (r * sin(t)), height_{image}, t, 0, 6.283185307179586) → d
  5. Vector(z_#, f_{(z#).}) → w
  6. CurveCartesian(t, 0, height_{image}, t, -5, 5) → Xh
  7. CurveCartesian(0, t, height_{image}, t, -5, 5) → Yh
  8. Textfield(z_*) → inputBox3
  9. Vector(z_#, z_1) → u
  10. Intersect(xAxis, yAxis) → A
  11. Vector(A, Δz) → v
  12. CurveCartesian((r * cos(t)), (r * sin(t)), t, t_a, t_b) → γ
  13. Textfield(t_a) → inputBox4
  14. Textfield(t_b) → inputBox5
  15. Sequence(t_a + (k / m * (t_b - t_a)), k, 0, m) → t_*
  16. Derivative(f, z) → df
  17. Vector(A, Δw) → h
  18. Vector(f_{(z#).}, f_{z1}) → g
  19. Vector(z_1, f_{z1}) → i
  20. Textfield(F) → InputBox1
  21. Vector(f_{(z#).}, Diff_#) → l